^{page 582 note *} That an unit-volume or particle of water consists of three times the number of chemical units or elements or minims, which other molecules in general consist of, is shown by the numbers of aeriform volumes which it and they respectively give. Thus, a volume of cold water gives from 1700 to 1728 volumes of steam, according to estimate, of which the third part is from 567 to 576. A volume of alcohol, when its vapour is heated up to the temperature of steam, gives 570 volumes. A volume of ether, supposing its aeriform units of volume to be dedoubled so as to assimilate it to water and alcohol, gives, at the same temperature, 2 × 285·9 = 572 volumes. And so in other cases, where at first sight there seems no relation. Thus, oil of turpentine gives, of the same temperature, only 193 volumes. But the formula of the unit of that liquid is C₂₀H₁₆ = 4(C₅H₄). It requires, therefore, to be multiplied by 3 to bring it up to the dodecatom, and render its vapour-volume comparable with the others. Now, 3 × 193 = 579, near enough the others. Good experiments in this field would be very valuable.

^{page 584 note *} I have here taken the atomic weights of this group of bodies as it stands in the unitary notation. But I must here add, that our molecular theory gives these numbers, not as atomic, but as molecular weights, proper to the smallest regular polyhedron, viz., the tetrahedron, so that the S, Se and Te of the unitary system are in ours, S₄, Se₄ and Te₄, while the O of the unitary system, which is truly an unit of oxygen gas, isin ours a coupled molecule= , or O₂. Sulphur as S₄ exists free, and unites with hydrogen and metals; and, in a word, functions as O. As S, on the other hand (being the alternate or reciprocal form of O), it unites with O, and when by itself forms an icosatom S₂₀, which is of course also the nucleus of (S₄)₂₀; but S₂₀ differs from (S₄)₂₀, at least when secularly consolidated, in possessing metallic lustre, and in being very stable, if not undecomposable. Its existence as a separate substance has only been obscurely detected. But for the sake of reference, it may be called Sulphurium; its symbol S₂₀= 8 × 20 = 160.

^{page 585 note *} The dedecaton and icosatom, when both are differentiated, that is X X₁₂X, X X₂₀X = 36X (the number of elements in AQ), gives, when divided by 2AQ, the same specific gravity as the compound dodecatom (X₁₂)₁₂=4 × 36X when divided by 8AQ.

^{page 589 note *} The relation between the atomic weights of these eminently active or basilous metals to each other and those of the principal constituents of the crust of the earth is very interesting. Thus, estimating their functioning by their respective attractions to the earth (their weights), the first, Lithium, simply by doubling and doubling again, gives nitrogen, aluminium, and iron, disregarding fractions in atomic weights, and taking the integers immediately above them,—

2Li=2 × 7=14 = N, Si and Al

4Li=4 × 7=28=Fe, and its companions.

Then the sulphide or deutoxide of each gives the metal in the series immediately above,—

Li =Li=7.

LiO₂ =Na=7 + 16=23.

NaO₂ =K=23 + 16=39.

Further, if we take Na at 24, and K at 40, which may be the primeval unreduced or full weights of these elemental bodies, then, by dedoubling, we obtain weights to complete the series,—

Thallium, in our theory, comes out a composite metal, of the type X X₂₀X. The body being sulphurium, the poles sodium, all locked together.

TI=Na S₂₀Na=23 + 160 + 23=206, or 208.